DISSERTATION 

PRESENTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  GRADUATE 

SCHOOL  OF  THE  OHIO  STATE  UNIVERSITY 


BY 

ALVA  W.  SMITH 


The  Ohio  State  University 
1921 


The  Effect  of  a  Superposed  Constant 
Field  Upon  The  Alternating  Current 
Permeability  and  Energy  Loss  In  Iron 


DISSERTATION 


PRESENTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FO« 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  GRADUATE 

SCHOOL  OF  THE  OHIO  STATE  UNIVERSITY 


BY 

ALVA  W.  SMITH 


- 


The  Ohio  State  University 
1921 


INTRODUCTION 

Investigations  on  the  effect  of  a  superposed  constant  induction 
upon  small  cyclic  changes  in  a  magnetic  substance  have  been  car- 
ried out  by  Rayleigh1,  Ewing2,  Gans3,  Madelung4,  Hoffman5,  Camp- 
bell6 and  others.  Much  of  the  systematic  work  in  this  field  has 
been  done  by  producing  small  cyclic  changes  by  sudden  increments 
and  decrements  to  the  existing  constant  field.  It  appeared  that 
further  study  might  profitably  be  made  with  alternating  current 
to  see  to  what  extent  the  constant  field  changes  the  permeability 
to  a  rapidly  alternating  field  and  whether  the  previous  history  in- 
fluences this  permeability  and  the  resulting  energy  losses  in  iron. 

Aside  from  its  bearing  upon  theories  of  magnetism,  this  prob- 
lem is  of  interest  from  a  technical  point  of  view.  In  the  double 
frequency  transformer,  the  telephone  receiver  and  in  numerous 
other  applications  of  the  polarized  electromagnet,  the  direct  cur- 
rent field  has  superposed  upon  it  an  alternating  field.  The  per- 
formance of  these  devices  is  conditioned  by  the  change  in  effective 
permeability  to  an  alternating  field  when  the  core  is  under  the 
magnetizing  action  of  this  constant  longitudinal  field. 


1.  Rayleigh,  Phil.  Mag.  23,  1887,  p.  225;  38,  1894,  p.  295. 

2.  Ewing  &  Klaassen,  Phil.  Tr.  A,  184,  1893,  p.  1030. 

3.  Gans,  Ann.  der  Phys.  27,  1908;  29,  1909;  33,  1910.     Phys.  Zeitsch.  1911; 
Ann.  der  Phys.  61,  1920. 

4.  Madelung,  Phys.  Zeitsch,  1912,  p.  436. 

5.  Hoffman,  Archiv.  f.  Electrotechnik,  1913,  p.  433. 

6.  Campbell,  Phys.  Soc.  of  London  Proc.     June,  1920. 


METHOD  OF  MEASUREMENT 

The  ratio  of  the  apparent  inductance  of  an  iron-cored  toroid  to 
the  inductance  of  the  same  coil  with  an  air  core  is  taken  as  the 
measure  of  the  alternating  current  permeability.  The  inductance 
which  the  coil  would  have  with  an  air  core  was  calculated  from 
the  number  of  turns  and  dimensions  of  the  coil.  Nearly  simul- 
taneous measurements  were  made  of  the  apparent  inductance  and 
resistance  of  the  iron  cored  coiL  The  difference  between  the  ap- 

G 


FIG.  1 


FIG.  2 

parent  resistance  measured  with  an  alternating  current  and  the 
true  resistance  measured  with  direct  current  is  the  increase  in 
resistance  due  to  core  losses.  This  increase  in  resistance  multi- 
plied by  the  square  of  the  effective  alternating  current  gives  the 
core  loss  due  to  the  combined  action  of  hysteresis  and  eddy  cur- 
. rents.  No  attempt  was  made  to  separate  these  losses. 

The  ordinary  or  normal  magnetization  curve  and  the  hysteresis 
loops  were  determined  by  ballistic  measurements.  By  means  of  a 
direct  current  in  winding  N2  (Figs.  1  and  2),  the  iron  core  was 

5 


brought  into  a  state  represented  by  a  given  point  on  one  of  these 
static  characteristics,  and  measurements  were  then  made  of  the 
apparent  inductance  and  resistance  of  winding  Nv  A  series  of 
such  readings  was  made  at  various  points  on  these  curves. 

Field  intensities  were  calculated  by  the  use  of  a  formula,  due  to 
Kirchhoff,  for  a  uniformly  wound  ring  of  n  turns  uniformly  mag- 
netized : 


1     /  a  \  3       1     /  a  \  5  ~| 

—  I  —  I    +—  I  —  |    +  —       gauss,    (1) 

12   \  R  /        80   \  R  /  J 


in  which  a  is  the  axial  breadth  and  R  the  mean  radius.  This 
formula  was  used  in  computing  both  the  direct  and  the  alternating 
current  fields.  In  the  latter  case  the  current  was  assumed  to  be 
of  sine  form  and  the  maximum  H  for  the  cycle  was  obtained  by 
substituting  for  I  in  Eqn.  I  the  meter  value  of  the  current  multi- 
plied by  the  square  root  of  two. 

Measurements  to  determine  the  alternating  current  permeabil- 
ity and  energy  loss  were  carried  out  by  two  methods.  In  the  first 
method,  the  impedance  bridge  shown  in  Fig.  1  was  used  to  obtain 
the  apparent  inductance  and  resistance  of  the  winding  N\  of  the 
ring  R.  For  G  three  different  generators  were  used,  giving 
frequencies  from  60  to  600  cycles  per  second.  All  of  these  gave 
nearly  sine  wave  electromotive  forces.  A  shunted  Duddell  thermo- 
galvanometer  was  used  at  A  to  measure  the  alternating  current 
through  Nj.  The  double-pole,  double  throw  switch  St  connects  N, 
into  the  bridge  arm  when  a  measurement  is  to  be  made  or  connects 
it  in  series  with  the  coil  Ct  of  a  transformer  when  the  ring  is  to 
be  demagnetized.  To  accomplish  this  C2  is  connected  to  the  labora- 
tory mains  and  is  placed  coaxially  upon  C^  Then  C2  is  gradually 
moved  to  a  considerabe  distance  from  Ct.  During  this  removal  of 
C2,  the  iron  is  assumed  to  be  carried  through  hysteresis  cycles  of 
constantly  diminishing  amplitude  and  is  finally  left  demagnetized. 

The  direct  current  to  produce  the  superposed  constant  field  is 
supplied  to  the  terminals  of  N2  by  a  storage  battery  B,  connected 
through  a  regulating  rheostat  W,  an  ammeter  Aiy  a  reversing 
switch  S2  and  several  retardation  coils  RET.  This  arrangement 
makes  it  possible  to  bring  the  iron  into  a  known  state  of  magneti- 
zation corresponding  to  points  on  the  previously  determined 
normal  curve  or  on  a  hysteresis  loop.  The  bridge  measurement  is 
then  made  with  a  small  alternating  current,  the  effective  value  of 
which  is  kept  constant  for  a  series  of  direct  current  fields.  The 
retardation  coils  so  completely  annul  the  alternating  current  in 

6 


the  direct  current  circuit  that  its  reaction  does  not  reduce  the  pri- 
mary inductance  by  more  than  one  percent. 

At  the  lower  frequencies  where  the  telephone  is  no  longer 
sufficiently  sensitive  in  making  bridge  balances,  the  electrometer 
method  of  measuring  inductance  previously  described  by  the  writer 
(Phys.  Rev.  Oct.  1919)  was  used.  In  this  method,  provision  is 
made  for  measuring  the  power  loss  in  Nx  (Fig.  2),  as  well  as  the 
inductance.  The  needle  of  the  electrometer  E  is  connected  to  the 
middle  of  the  high  resistance  HR,  the  halves  of  which  are  two  ex- 
actly similar  coils  of  50,000  ohms  resistance. 

When  an  inductance  measurement  is  to  be  made,  the  quadrants 
of  the  electrometer  are  connected  across  the  capacity  C,  and  N! 
is  connected  into  the  gap  S2.  The  alternating  current  registered 
by  A  is  regulated  by  means  of  the  rheostat  Rh  to  the  desired  value 
and  the  electrometer  deflection  observed.  The  inductance  stand- 
ard Ls  is  then  substituted  for  Nx  in  the  gap  S2,  the  current  regu- 
lated to  its  previous  value  and  the  electrometer  deflection  again 
read.  The  two  inductances  are  directly  proportional  to  their 
respective  deflections.  In  other  respects,  this  method  is  like  the 
bridge  method. 

To  measure  the  power  loss  in  Nlt  the  electrometer  quadrants  are 
connected  across  the  non-inductive  resistance  R1?  and  N!  is  con- 
nected into  the  gap  S2.  The  alternating  current  is  regulated  to  the 
desired  value  and  the  electrometer  deflection  read.  Then  the 
known  resistance  Rs  is  substituted  for  Nx,  the  current  regulated 
to  its  previous  value  and  the  electrometer  deflection  again  read. 
The  ratio  of  the  effective  resistance  of  Nt  to  the  resistance  of  Rs 
is  equal  to  the  ratio  of  these  respective  deflections^ 

The  bridge  method  is  the  more  convenient  for  the  smaller  cur- 
rents and  higher  frequencies,  where  its  sensibility  far  exceeds  that 
of  the  second  method.  On  the  other  hand,  the  lack  of  sensitivity 
at  lower  frequencies  gives  the  relative  advantage  to  the  electro- 
meter method,  particularly  for  the  larger  currents,  for  the  deflec- 
tions are  proportional  to  the  square  of  the  current,  other  factors 
being  the  same. 

Each  measured  value  of  inductance  was  divided  by  the  in^ 
ductance  of  the  same  toroid  with  an  air  core  to  obtain  the  per- 
meability of  the  iron.  Two  methods  of  calculating  this  inductance 
were  used.  In  the  first  of  these,  the  following  equation  was  used: 

n  A  H 

L  =  -      —  henrys    (2) 

10s  I 


1  F.  M.  Laws,  Elect.  Measurements,  p.  322. 

7 


A  is  the  sectional  area  of  the  iron  core,  n  is  the  number  of  turns 

H 

in  N!,  and  —  is  obtained  from  Eqn.  1.    The  second  formula  used 
I 

in  calculating  the  inductance  is  taken  from  the  Bulletin  of  the 
Bureau  of  Standards,  Vol.  S,  No.  1.    It  is  — 


L  =  2  n1 


a  log  —  henrys 
r, 


(3) 


In  this  formula,  a  is  the  axial  thickness  and  r2  and  rx  are 
respectively  the  outer  and  the  inner  radii  of  the  ring.  The  dif- 
ference between  the  values  calculated  by  the  two  methods  was  of 
the  order  of  one-fourth  of  one  percent.  The  calculated  values  are 
recorded  in  Table  I. 

TEST  PIECES 

Three  different  specimens  of  iron  showing  widely  different  mag- 
netic properties  were  studied.  Each  test  piece  was  in  the  form  of 
a  ring.  Ring  I  was  built  up  from  stampings  of  transformer  plate 
of  16  mils  thickness.  The  plates  were  given  a  thin  layer  of  shellac, 
dried  and  assembled.  A  single  layer  of  tape  was  applied  to  hold 
the  plates  together  and  over  this  were  wound  two  windings  of  a 
single  layer  each  of  double  silk  covered  No.  21  magnet  wire.  Ring 
II  was  similarly  prepared  except  that  dynamo  plate  was  used. 
Ring  III  was  made  by  placing  two  dust  cores  with  their  faced 
surfaces  together.  These  cores  are  prepared  by  treating  powdered 
electrolytic  iron  with  shellac  and  compressing  into  the  form  of 
rings1. 

TABLE  I 


Ring 

No.  of 
Plates 

Radial 
Thick- 
ness in 
CM. 

Axial 
Thick- 
ness in 
CM. 

Mean 
Diam. 
in  CM. 

Turns 
inN, 

Turns 
inN, 

Induct 
of  N,  Mil- 
henry 

I 

54 

0.952 

2.255 

14.11 

473 

437 

0.136 

II 

28 

0.635 

0.995 

9.29 

302 

293 

0.247 

III 

2 

2.15 

0.535 

7.55 

190 

183 

0.0458 

1  Speed  and  Elmen,  Jour.  A.  I.  E.  E.,  July,  1921. 

8 


RESULTS 

Static  Curves.  In  Fig.  3,  the  normal  magnetization  curves  and 
hysteresis  loops  for  Rings  I  and  II  are  given.  The  permeability  of 
I  rises  to  a  maximum  of  4200  at  H  =  1 . 3'  gauss ;  that  of  II  to  a 
maximum  of  1430  at  H  =  5 . 1  gausses.  The  remanent  magnetism 
is  nearly  the  same  for  both,  but  the  coercive  force  for  Ring  II  is 
more  than  twice  as  great  as  for  Ring  I.  For  a  range  of  B  max. 
from  7400  to  12000,  the  hysteresis  loss  for  Ring  I  obeys  the  para- 
bolic law,  and  has  a  Steinmetz  exponent  of  2.13;  but  for  flux 
densities  above  12000,  the  losses  appear  to  increase  faster  than 


Ballidc 


I  Nori 


ZHy&rtii 
3  Per/r     ' 

X-Ti-oo 


lC 

rtsisLook 


j  lust  Core 


g 
.3C5Z- 


Y 
M 


FIG.  3 


n 

* ' 


FIG.  4 


would  be  predicted  by  this  law.    Ring  II  gives  a  value  of  1 . 69  for 
this  exponent. 

The  magnetic  characteristics  of  the  dust  core,  (Fig.  4),  are 
strikingly  different  from  those  of  the  first  two  test  rings.  The 
normal  curve  shows  an  inclination  to  bend  at  low  fields  like  any 
other  sample  of  iron.  But  from  60  gausses  up  to  101  gausses,  the 
upper  limit  studied,  the  B-H  curve  is  nearly  linear.  The  permea- 
bility rises  from  22 . 6  at  a  field  intensity  of  one  gauss  to  35 . 5  at 
fifty  gausses,  beyond  which  it  remains  nearly  constant.  Hysteresis 
loops  for  this  specimen,  with  values  of  B  max.  from  630  to  3200, 
show  that  the  remanent  induction  for  each  loop  is  from  8  to  10 
per  cent  of  its  maximum  induction.  For  the  smallest  loop,  the 
coercive  force  is  10  per  cent  of  the  maximum  field  intensity;  but 

9 


for  each  of  the  other  loops  for  B  max.  greater  than  900,  the 
coercive  force  is  uniformly  13  per  cent  of  the  maximum  field  in- 
tensity. 

In  the  lower  half  of  Fig.  4,  the  logarithms  of  the  areas  of  these 
loops  are  plotted  against  the  logarithms  of  the  maximum  and  in- 
ductions. From  this  graph  the  following  facts  can  be  deduced: 
(1)  the  hysteresis  loss  for  these  dust  cores  obeys  the  parabolic 
law;  (2)  the  Steinmetz  exponent  of  Bm  is  2.09;  (3)  the  coefficient 
is  0.0005. 

The  relatively  low  and  nearly  constant  permeability  of  these  dust 
cores  is  probably  due  to  a  reduction  of  the  effective  cross  section 
of  the  core  by  filling  the  interstices  between  the  finely  divided  iron 
particles  with  a  non-magnetic  substance. 


A.G  Field  fi',g. 


Auction 


Fre, '.  500~ 


FIG.  5 

Permeabilities  and  Losses  with  no  Superposed  Direct  Current 
Field.  The  results  obtained  with  Ring  I  demagnetized  and  with 
no  direct  current  induction  are  given  in  Fig.  5.  From  an  initial 
value  of  250,  the  alternating  current  permeability  rises  to  what 
appears  to  be  a  maximum  at  a  value  of  about  one-fifth  of  the  maxi- 
mum direct  current  permeability. 

Each  maximum  value  of  the  alternating  field  is  multiplied  by 
.he  corresponding  value  of  the  permeability  to  obtain  the  maxi- 
mum value  of  the  induction.  The  logarithms  of  these  inductions 
are  plotted  in  the  insert  in  Fig.  5  against  the  logarithms  of  the 
measured  iron-losses  at  these  inductions.  The  equation  of  the 
curve  is  of  the  form  W  =  k  Bma. 

From  this  curve  a  =  2 . 13.  From  a  similar  curve  for  Ring  II, 
for  H  from  .025  to  3 . 5  gausses,  a  =  2 . 35.  The  alternating  cur- 

10 


rent  permeability  for  Ring  II  rises  from  an  initial  value  of  100  to 
a  value  of  525  at  H  =  3 . 5  without  indications  of  a  maximum. 

For  Ring  I,  the  exponent  of  Bm  in  the  above  equation  is  near 
to  the  value  2.16,  which  is  the  exponent  of  Bm  from  ballistic 
measurements.  For  Ring  II  the  exponent  for  the  total  loss  is  2 . 35 ; 
for  the  hysteresis  loss  alone  it  is  1 . 69  from  the  static  curves.  It 
was  not  expected  that  these  two  exponents  should  be  the  same  for 
the  reasons  that  they  cover  a  different  range  of  inductions;  the 
alternating  current  loss  includes  eddy  current  losses;  and  the 
actual  shapes  of  the  hysteresis  loops  for  very  slow  cycles  is  very 
different  from  those  for  very  rapid  cycles,  as  was  shown  by 
Ewing.1 


Alternating  CurrcritPetmeability.Westert>E.lccfncDv 


&0 


24.5 


NoD.C. 


S00 


ZlS 


HiffQt 


A.CFiel  1. . 


.^onstant^ld.    ^ 


FIG.  6 


In  the  upper  part  of  Fig.  6,  the  alternating  permeability  of  the 
dust  core  at  500  cycles  per  second  with  no  superposed  field  is  given 
as  a  function  of  the  maximum  value  of  the  alternating  field.  The 
initial  value  of  the  permeability  is  22.1  and  the  value  reached  at 
4.5  gausses  is  25.0.  Ballistic  tests  give  a  value  of  22.6  for  the 
initial  permeability  and  data  supplied  by  the  Western  Electric  Co. 
give  22  .  1  for  its  value  at  H  =  1  gauss  and  1000  cycles  per  second. 
The  very  small  change  of  permeability  with  frequency  can  be  at- 
tributed to  a  rather  complete  elimination  of  eddy  currents  on  the 
one  hand  and  on  the  other  to  the  introduction  of  a  substance  with 
nearly  constant  reductivity  between  the  particles  of  iron. 


1  Loc.  cit. 


11 


The  Effect  of  a  Superposed  Constant  Induction.  The  dependence 
of  the  alternating  permeability  upon  the  direct  current  induction 
for  Rings  I  and  II  is  shown  by  the  lower  groups  of  curves  of  Figs. 
7  and  8  respectively.  The  permeabilities  are  plotted  as  ordinates 
and  the  superposed  inductions  on  the  normal  magnetization  curve 
as  abscissae.  The  permeability  falls  rapidly  with  small  direct  cur- 
rent inductions  to  a  certain  point  after  which  the  decrease  is  more 
gradual.  The  abrupt  change  in  slope  appears  to  come  where  the 
direct  current  field  has  increased  to  such  a  point  that  the  resultant 
of  the  direct  current  and  alternating  current  fields  no  longer  as- 
sumes negative  values,  or  in  other  words  where  the  field  ceases  to 
be  alternating  and  becomes  pulsating. 


FIG.  7 


FIG.  8 


For  different  values  of  alternating  field,  the  permeabilities  differ 
most  from  each  other  when  there  is  no  direct  current  induction. 
With  increasing  direct  current  inductions  these  curves  converge. 
Beyond  the  point  of  convergence  the  permeability  is  practically 
independent  of  the  alternating  current  induction.  Campbell1  has 
recently  published  data  showing  a  rise  of  permeability  with  small 
superposed  direct  current  fields.  I  have  not  observed  this  rise  in 
any  of  my  samples. 

From  the  lower  part  of  Fig.  6  one  sees  that  the  superposed  di- 
rect field  has  much  less  influence  upon  the  alternating  permeability 


1  Loc.  cit. 


12 


of  the  dust  core  than  upon  the  other  specimens.  With  a  direct  field 
of  forty  gausses,  its  permeability  has  decreased  only  5  per  cent  of 
its  original  value ;  with  a  field  of  only  twelve  gausses  that  of  Ring 
I  has  decreased  from  90  to  95  per  cent  of  its  original  value  with 
no  superposed  field. 

A  typical  set  of  data  for  Ring  I  is  given  in  Table  II.  These  data 
are  taken  at  points  on  the  normal  magnetization  curve  and  are 
plotted  in  Fig.  7,  curve  4. 

TABLE  II 


Ha.c.=  .094 

Freq.  =  500  cycles  per  sec. 

Hd.c.  gauss 

M  a.c. 

Bd.c.  x  Ma.c. 

Energy  loss 
microwatts 

0 

386 

0 

1695 

0.37 

344 

120 

1070 

0.56 

329 

313 

1000 

0.99 

249 

995 

650 

1.43 

199 

1175 

382 

2.48 

132 

1135 

146 

3.84 

94 

940 

78.5 

5.82 

68 

760 

39.3 

7.45 

57.5 

675 

27.2 

10.46 

45.0 

558 

15.1 

The  Force  Function.  In  his  discussion  of  the  telephone  receiver 
Rayleigh  makes  use  of  Maxwell's  equation  for  the  force  action  of 
an  electro-magnet  upon  its  armature.  Assume  that  this  force  per 
unit  area  of  pole  face  is  given  by 


(4) 


If  we  consider  the  induction  B  as  due  to  a  constant  component 
B0  and  an  alternating  induction  Bm  sin  <ot  produced  by  a  current 
Im  sin  wt,  we  can  write 

Bm2         Bm2 

F  =  K  (B0-  +  2B0Bm  sin  «t  -\ cos  2o/t)  .  .  (5) 

2  2 

From  this  equation  it  appears  that  the  force  consists  of  three 

B  - 

J-»m 

components,  one  a  constant  force  proportional  to    (B02  -\ ); 


a  second, 

t 

F,  =  2KB0Bm  sin  <ut 


(6) 


of  the  same  frequency  as  the  current ;  and  a  third 

13 


K 

F3  =  —  Bm2  cos  2«,t (7) 

2 


of  double  the  frequency  of  the  current. 
If  in  Eqn.  (6),  for  Bm  we  substitute 

Bm  =  Hm/ia.c.  =  K2Im/xa.c 

in  which  K2  is  a  constant,  we  get 

F2  =  2KK,  B0/Aa.c.  Im  sin  «t 

The  change  in  force  per  unit  current  is  therefore 


(8) 
(9) 


dF, 


dL 


=  2KK 


D  C  Induction  inKilotjau 

FIG.  9 


.c.  sin  o>t. 


(10) 


The  quantity 


dF, 


dL 


is  a  measure  of  the  force  sensitivity  of  the 


polarized  electromagnet.  Equation  (10)  states  that  the  change 
in  pull  per  unit  current  of  the  same  frequency  is  proportional  to 
the  product  B0x^a.c.  To  make  the  response  of  the  same  frequency 
as  the  current  as  large  as  possible  it  is  necessary  that  this  product 
be  a  maximum. 

The  upper  family  of  curves  in  Figs.  7  and  8  shows  the  de- 

14 


pendence  of  this  product  upon  the  direct  current  induction  for 
Rings  I  and  II  respectively.  The  maxima  of  these  occur  near  the 
inductions  for  which  the  direct  current  permeability  is  a  maxi- 
mum. 

An  increase  in  the  direct  current  induction  up  to  the  point  of 
maximum  force  sensitivity  is  accompanied  by  a  considerable  de- 
crease in  the  alternating  current  permeability  and  hence  a  decrease 
in  Bm  in  Eqn.  7  for  a  given  alternating  current.  This  decrease  in 
Bm  results  in  a  decrease  in  the  distortion  of  the  pull  arising  from 
the  double  frequency  term.  Furthermore,  it  is  of  interest  to  note 
that  the  iron  loss  (Fig.  9)  at  the  induction  for  which  the  force 


function  is  a  maximum  is  only  a  small  fraction  of  its  value  with 
no  superposed  field,  the  alternating  field  remaining  constant. 

The  curves  of  Fig.  9  show  the  variation  of  the  total  iron  loss  as 
a  function  of  the  direct  current  induction  for  an  alternating  field 
of  0.9  gauss  at  frequencies  of  62,  128  and  500  cycles  per  second. 
Each  curve  shows  that  there  is  a  decrease  in  the  iron  loss  when 
the  direct  current  induction  is  increased  and  the  alternating  cur- 
rent field  kept  at  a  constant  maximum  value.  By  means  of  his 
hysteresis  tracer  Ewing  traced  the  small  cycles  produced  by  a 
given  cyclic  field  when  a  constant  field  is  superposed.  He  found 
that  these  small  loops  decrease  in  area  as  the  direct  current  in- 
duction is  increased.  This  decrease  in  area  of  these  diminutive 

15 


loops  results  in  a  decreased  iron  loss.  The  diminution  in  area  of 
the  loops  is  to  be  associated  with  the  decrease  in  permeability  re- 
sulting from  the  restraint  imposed  upon  the  elementary  magnets 
by  the  constant  field.  A  decrease  in  permeability  would  cause  a 
decrease  in  the  eddy  current  loss  also. 

The  curves  of  Fig.  10  were  taken  with  an  alternating  field  of 
0.98  gauss  for  different  frequencies.  The  variation  of  permeabil- 
ity with  frequency  appears  to  be  greatest  with  no  superposed  field 
and  nearly  to  disappear  when  the  direct  current  field  is  increased 
to  a  point  where  saturation  occurs. 

Fig.  11  shows  the  variation  of  the  permeability  with  the  direct 
current  field  for  points  on  the  hysteresis  loop  of  Fig.  3.  To  trace 
this  curve,  start  at  the  upper  extremity  of  the  loop  with  the  field 
a  maximum.  The  permeability  at  this  point  is  given  by  the  point 


FIG.  11 

on  the  curve  at  the  extreme  right  of  Fig.  11.  As  the  direct  current 
field  is  reduced  to  zero,  the  permeability  increases  along  the  lower 
of  the  curve  to  the  right  of  the  axis.  As  the  field  is  increased  in 
the  opposite  direction  the  permeability  continues  to  increase  and 
reaches  a  sharp  maximum  from  which  it  falls  rapidly,  finally 
reaching  the  point  on  the  curve  at  the  extreme  lower  left  of  Fig. 
11  as  the  field  is  increased  to  a  maximum  in  this  direction.  The 
returning  branch  of  the  permeability  curve  starting  from  this 
point  corresponds  to  the  remaining  half  of  the  hysteresis  loop 
starting  at  the  lower  extremity  of  the  loop. 

For  comparison,  permeabilities  on  the  normal  curve  are  plotted 
on  the  same  graph.  For  the  demagnetized  specimen  (Hd.c.  =  0) 
the  permeability  reaches  a  value  of  386.  With  increasing  fields  the 
permeability  diminishes  in  such  a  way  that  the  curve  coincides 
with  a  part  of  the  curve  for  the  ascending  branch  of  the  hysteresis 

16 


loop.  Residual  magnetism  has  reduced  the  permeability  from  386, 
the  value  on  the  normal  curve,  to  160. 

Similar  curves  have  been  made  with  an  alternating  field  as  large 
as  0.9  gauss.  In  this  case  the  effect  of  the  residual  magnetism 
was  apparently  neutralized  by  the  demagnetizing  action  of  the 
alternating  current  field.  The  two  maxima  of  the  permeability 
curves  coalesce  on  the  permeability  axis,  and  the  permeability 
curve  for  points  on  the  normal  curve  intersects  the  axis  at  the 
same  point.  The  ascending  and  descending  branches  of  the  per- 
meability curve  are  brought  nearer  together  than  they  are  in  Fig. 
11,  but  do  not  coincide. 

In  Fig.  12,  curve  1  gives  the  variation  of  the  permeability  with 
the  direct  current  induction  for  points  on  the  hysteresis  loop,  the 
direction  of  tracing  the  permeability  loop  being  indicated  by  the 


FIG.  12 

direction  of  the  arrow.  In  curve  2  the  permeability  for  the  normal 
curve  is  replotted.  From  these  curves  and  Fig.  11,  it- appears  that 
the  permeability  is  not  a  simple  function  either  of  the  superposed 
field  or  induction,  but  is  affected  by  the  previous  magnetic  history. 
Curve  3,  of  Fig.  12  represents  the  dependence  of  the  iron  loss  upon 
the  direct  current  induction  for  points  on  the  hysteresis  loop.  The 
form  of  the  curve  is  similar  to  that  of  the  permeability  curve, 
which  is  further  evidence  that  the  change  in  iron  loss  is  due  to 
the  change  in  permeability.  A  similar  set  of  curves  for  Ring  II  is 
given  in  Fig.  13.  A  curve  of  iron  loss  for  the  normal  magnetiza- 
tion curve  has  been  added  to  this  group. 

Oscillograms  were  made  of  current  through  the  voltage  across 
the  winding  of  Ring  I  with  the  ring  first  demagnetized  and  then 
with  progressively  larger  currents  in  the  direct  current  winding. 
With  no  superposed  direct  current,  the  current  wave  showed  the 

17 


characteristic  distortion  due  to  hysteresis.    As  the  direct  current 
was  increased  the  distortion  decreased  and,  when  the  direct  cur- 


FIG.  13 

rent  required  for  saturation  was  reached,  the  distortion  had  en- 
tirely disappeared. 

The  force  function,  Bd.c.xo>a.c.,  for  points  on  the  normal  curve 


Nora 


•>  K, i  lay 


Looft 
auss 


FIG.  14 

and  upon  the  hysteresis  loop  have  been  plotted  in  Fig.  14  against 
the  direct  current  induction.  From  curve  B  it  is  seen  that  this 
force  function  increases  to  a  maximum  as  the  induction  decreases 

18 


from  the  maximum  value  to  the  remanent  value;  and  that  this 
product  decreases  to  zero  as  the  induction  becomes  zero.  As  the 
induction  increases  to  a  maximum  in  the  opposite  direction  this 
product  follows  the  lower  curve  to  the  left  of  the  axis  of  Fig.  14, 
passing  through  a  second  maximum  of  roughly  half  the  value  of 
the  first  maximum.  The  maximum  value  attained  by  this  product 
on  the  normal  curve  is  intermediate  in  value  between  the  maxi- 
mum reached  on  either  branch  of  the  hysteresis  loop. 

SUMMARY 

(1).  The  ordinary  hysteresis  loss  for  very  slow  cycles  and 
moderate  inductions  obeys  the  parabolic  law  for  all  of  the  speci- 
mens studied. 

(2).  The  total  iron  losj  for  rapid  cycles  is  a  parabolic  function 
of  the  alternating  current  induction,  when  there  is  no  superposed 
direct  field. 

(3).  When  there  is  no  superposed  constant  field,  the  major 
part  of  the  apparent  change  of  permeability  with  frequency  is  due 
to  the  action  of  eddy  currents. 

(4).  For  a  given  value  of  alternating  field  the  permeability 
and  the  iron  loss  each  decreases  as  the  direct  current  magnetiza- 
tion is  increased  from  the  demagnetized  state;  and  when  the  iron 
is  carried  slowly  through  a  hysteresis  cycle,  the  permeability  and 
energy  loss  pass  through  cycles.  Each  quantity  reaches  a  maxi- 
mum when  the  value  of  the  direct  current  induction  is  equal  to 
the  remanent  value. 

(5).  For  small  values  of  alternating  field,  the  force  function 
Bd.c.x/ia.c.  passes  through  two  unequal  maxima,  on  each  branch  of 
the  hysteresis  loop.  It  reaches  on  the  normal  magnetization  curve 
a  maximum  value  intermediate  between  the  maxima  on  the 
hysteresis  loop. 

(6).  The  iron  loss  at  the  point  at  which  the  force  function  is 
a  maximum  is  relatively  small. 

(7).  For  the  three  specimens  on  which  observations  have  been 
made  it  is  found  that  the  magnitude  of  the  effect  of  the  superposed 
constant  magnetic  field  is  a  function  of  the  permeability  of  the 
specimen.  The  lower  the  permeability  the  smaller  is  the  effect  of 
the  superposed  field. 

In  conclusion,  I  wish  to  thank  Professor  Alpheus  W.  Smith  for 
many  helpful  suggestions  during  the  progress  of  this  work.  I  de- 
sire to  acknowledge  also  my  indebtedness  to  Dr.  H.  D.  Arnold  of 
the  Western  Electric  Company  who  kindly  supplied  me  with  the 
dust  cores. 

19 


AUTOBIOGRAPHY 

I,  Alva  Wellington  Smith,  was  born  in  Fayette,  Ohio,  August 
26,  1885.  I  received  my  preparatory  education  at  the  Fayette 
Normal  and  at  the  Michigan  State  Normal;  my  undergraduate 
education  at  the  Ohio  State  University,  from  which  I  received  the 
degree  of  Bachelor  of  Arts  in  1912  and  the  degree  of  Master  of 
Arts  in  1914.  I  served  on  the  corps  of  research  engineers  of  the 
Western  Electric  Company  during  the  year  1914-1915.  I  was 
an  asistant  in  physics  at  the  Ohio  State  University  from  1912  to 
1914  and  an  instructor  at  the  same  institution  from  1915  to  1921. 
My  post  graduate  education  was  received  at  the  University  of 
Chicago  and  at  the  Ohio  State  University  from  which  I  received 
the  degree  of  Doctor  of  Philosophy  in  1921. 


21 


demand  ma  - 


demand  may  be  renewed  if  Lnf-^ay'     Books  not  in 
^pn-ation  of  loan  period.       apphcatlon   is  made  before 


binder 
Gaylord  Bros. 

Makers 
Syracuse,  N.  y 

W.  JAN  21,  1908 


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